“The thigh was considered the source of posterity in the ancient world. Or, more properly, the “loins” or the testicles. The phrase “under the thigh” could be a euphemism for “on the loins.” There are two reasons why someone would take an oath in this manner: 1) Abraham had been promised a “seed” by God, and this covenantal blessing was passed on to his son and grandson. Abraham made his trusted servant swear “on the seed of Abraham” that he would find a wife for Isaac. 2) Abraham had received circumcision as the sign of the covenant (Genesis 17:10). Our custom is to swear on a Bible; the Hebrew custom was to swear on circumcision, the mark of God’s covenant. The idea of swearing on one’s loins is found in other cultures, as well. The English word testify is directly related to the word testicles.”

www.gotquestions.org/hand-under-thigh.html